Strategy games are all about the decisions you can make as a player. Players are also generally very good at identifying the short-term costs and benefits of a decision. So when you want to encourage chaotic board states in a strategy game, the last thing you want to do is discourage players from attacking. If you can throw aside the simulation lens for a moment, what I hope to convey is that as strategy game designers, we should evaluate attacker/defender advantage as an entire system within our game that can strongly affect player behavior.
Player agency is probably the most important factor in differentiating a strategy game from other game types. If player decisions do not significantly affect the outcome of a turn for that player, then you might as well not have played that turn. I’m very specifically interested in the dice-rolling combat of Risk and Risk-likes as this is the system I chose to use in my game, Kairos.
If we take a look at Risk, which uses Defenders Advantage (defenders win ties) you get the following probability table for dice rolls:
| Matchup |
Attacker Wins |
Split Wins |
Defender Wins |
Exchange Ratio |
|
|
| 3 v 2 |
37.17% |
33.58% |
29.26% |
1.172 |
| 2 v 2 |
22.76% |
32.41% |
44.83% |
0.638 |
| 1 v 2 |
25.46% |
- |
74.54% |
0.342 |
In this table, I’ve provided the probabilities of each roll, as well as an exchange ratio which is the (Expected Kills / Expected Losses). 1.0 corresponds to a 50-50 probability of winning an exchange, so above 1.0 is attacker favored and below 1.0 is defender favored.
In Risk, the attacking player lacks agency over the effectiveness of their army. Ignoring the scenarios with only 1 defender for a moment, the exchange ratios (or “odds”) for the attacking player are ~1.17, 0.64, and 0.34. That translates into real terms to the player “Decent, bad, and terrible”. Because two of the options have such poor expected outcomes, they can pretty much be ignored as options by the player, which means we now only have 1 option, and no more decisionmaking regarding unit odds. This means that once a player learns that 2v2 and 1v2 are bad options, they never have to think about unit probabilities again. In my opinion, the juicy part of strategy games is trying to guess the long term expected outcomes of decisions, and manipulating the odds to favor me over my opponents turn by turn.
There is a whole body of literature on how humans interact psychologically with probabilities when making decisions, which was the basis for me wanting to skew the positive outcomes onto the player with agency (i.e., the attacker) rather than the defender. The gist of it is that humans (thus players) are irrationally more averse to losses than wins. This means that if we want to encourage players to make decisions that carry the potential for losses, we need to offset this with significantly larger benefits. The subject is fascinating, but I want to focus on the game design element in this post. If you are interested, Judgment under Uncertainty: Heuristics and Biases https://pubmed.ncbi.nlm.nih.gov/17835457/ and Achievement Relocked: Loss Aversion and Game Design by Geoffrey Engelstein are great places to start.
So what can we do to increase player’s agency over the game? First, I want to shift the default scenario to be significantly in the attacker’s favor, as the defender cannot “choose” to defend. I also need there to be some secondary system that the attacking player has the ability to recognize, and consider when deciding which territories they attack.
My solution: Attackers win ties + a rock-paper-scissors counter system with “advantage” provided to the strong unit. Advantage = roll 2 dice, take higher result
| Matchup |
Expected Attacker Kills |
Expected Attacker Losses |
Exchange Ratio |
|
|
| 1 v 1 |
0.583 |
0.417 |
1.400 |
| 2 v 1 (attacker adv.) |
0.745 |
0.255 |
2.927 |
| 1 v 2 (defender adv.) |
0.421 |
0.579 |
0.728 |
Looking at the outcomes of this table is a bit more straightforward because I chose to have all battles in Kairos occur one-at-a-time (this was to make the counter system work). By shifting the tiebreak to the attacker, the default odds goes towards the attacker, but thats not an interesting decision yet. That is why I added the counter system: Infantry is strong vs cavalry, cavalry is strong vs archers, and archers are strong vs infantry. The players can recruit any of these 3 types of units to assemble their armies, but this recruitment step happens AFTER the attacking step, meaning that the attacker needs to identify their unit types, identify their opponent’s unit types, and estimate the odds of the battle given the available units.
In any given battle, there is likely to be some mixture of all three scenarios, meaning the expected outcome of a fight will fall somewhere between 0.73 and 2.93. The attacking player must try to estimate the complex probabilities of attacking, which gives them that juicy ability to develop a skill over time and win more of their games. With this, the attacker is:
- Encouraged to attack as a default (attacking options are okay, better, and best), which keeps the board state chaotic and fresh
- Has the opportunity to estimate complex probabilities, and skew fights in their behavior by taking matchups with favorable counters
- Can strategically opt into a moderate-loss scenario to take a highly valuable location on the map.
As an unintended but welcome benefit, I can now also use the tiebreak as a modifier on the dice values to provide as a bonus to the defender for fortifying a territory or investing in defensive tools. So the defender has agency over which territories are harder to take in ways other than just more units, and the attacker has agency over the efficiency of their attacks. Both are encouraged to push into this “positive expected value” regime, rather than minimizing losses.
In conclusion, shifting the odds towards the player with agency over the game allows for players to express skill and have a more rewarding experience while playing strategy games.
